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<div class="chapter">
<div class="titlepage"><div>
<div><h2 class="title">
<a name="yap"></a>Chapter 44. Boost.YAP</h2></div>
<div><div class="author"><h3 class="author">
<span class="firstname">Zach</span> <span class="surname">Laine</span>
</h3></div></div>
<div><p class="copyright">Copyright © 2018 T. Zachary Laine</p></div>
<div><div class="legalnotice">
<a name="yap.legal"></a><p>
        Distributed under the Boost Software License, Version 1.0. (See accompanying
        file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
      </p>
</div></div>
</div></div>
<div class="toc">
<p><b>Table of Contents</b></p>
<dl class="toc">
<dt><span class="section"><a href="yap.html#boost_yap.introduction">Introduction</a></span></dt>
<dt><span class="section"><a href="boost_yap/manual.html">Manual</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="boost_yap/manual.html#boost_yap.manual.an_expression_template_primer">An Expression
      Template Primer</a></span></dt>
<dt><span class="section"><a href="boost_yap/manual.html#boost_yap.manual.the_yap_way">The YAP Way</a></span></dt>
<dt><span class="section"><a href="boost_yap/manual.html#boost_yap.manual.expressions">Expressions</a></span></dt>
<dt><span class="section"><a href="boost_yap/manual.html#boost_yap.manual.mix_and_match_expression_templates">Mix-and-Match
      Expression Templates</a></span></dt>
<dt><span class="section"><a href="boost_yap/manual.html#boost_yap.manual.kinds_of_expressions">Kinds of Expressions</a></span></dt>
<dt><span class="section"><a href="boost_yap/manual.html#boost_yap.manual.operators">Operators</a></span></dt>
<dt><span class="section"><a href="boost_yap/manual.html#boost_yap.manual.transforming_expressions">Transforming
      Expressions</a></span></dt>
<dt><span class="section"><a href="boost_yap/manual.html#boost_yap.manual.evaluating_expressions">Evaluating Expressions</a></span></dt>
<dt><span class="section"><a href="boost_yap/manual.html#boost_yap.manual.operator_macros">Operator Macros</a></span></dt>
<dt><span class="section"><a href="boost_yap/manual.html#boost_yap.manual.how_expression_operands_are_treated">How
      Expression Operands Are Treated</a></span></dt>
<dt><span class="section"><a href="boost_yap/manual.html#boost_yap.manual.printing">Printing</a></span></dt>
<dt><span class="section"><a href="boost_yap/manual.html#boost_yap.manual.examples">Examples</a></span></dt>
<dt><span class="section"><a href="boost_yap/manual.html#boost_yap.manual.header_organization">Header Organization</a></span></dt>
<dt><span class="section"><a href="boost_yap/manual.html#boost_yap.manual.configuration">Configuration</a></span></dt>
<dt><span class="section"><a href="boost_yap/manual.html#boost_yap.manual.object_code">Object Code</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="boost_yap/concepts.html">Concepts</a></span></dt>
<dt><span class="section"><a href="boost_yap/compiler_support.html">Compiler Support</a></span></dt>
<dt><span class="section"><a href="boost_yap/dependencies.html">Dependencies</a></span></dt>
<dt><span class="section"><a href="yap/reference.html">Reference</a></span></dt>
<dd><dl><dt><span class="section"><a href="yap/reference.html#headers">Headers</a></span></dt></dl></dd>
<dt><span class="section"><a href="boost_yap/rationale.html">Rationale</a></span></dt>
</dl>
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="boost_yap.introduction"></a><a class="link" href="yap.html#boost_yap.introduction" title="Introduction">Introduction</a>
</h2></div></div></div>
<p>
      "I like to start documentation with a quote. A nice, pithy one."
    </p>
<p>
      <span class="emphasis"><em><span class="bold"><strong>— Eric Niebler (paraphrased)</strong></span></em></span>
    </p>
<h4>
<a name="boost_yap.introduction.h0"></a>
      <span class="phrase"><a name="boost_yap.introduction.motivation"></a></span><a class="link" href="yap.html#boost_yap.introduction.motivation">Motivation</a>
    </h4>
<p>
      Expression templates are rad. They are used in lots of libraries; here are
      just three of the most impressive:
    </p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          <a href="http://boost-spirit.com" target="_top">Boost.Spirit</a> allows you to
          write an EBNF-style grammar that gets transformed into a PEG parser.
        </li>
<li class="listitem">
          <a href="http://eigen.tuxfamily.org" target="_top">Eigen</a> allows you to do
          linear algebra using a very natural and mathematical expression syntax
          that <a href="http://eigen.tuxfamily.org" target="_top">Eigen</a> uses to heavily
          optimize your expressions.
        </li>
<li class="listitem">
          <a href="https://www.lri.fr/~falcou/nt2" target="_top">NT2</a> takes slightly
          modified MatLab code and allows it to be parsed and run as highly optimized
          C++ code.
        </li>
</ul></div>
<p>
      However, this can come at a high cost. Expression templates are costly to implement
      and maintain. Each of <a href="http://eigen.tuxfamily.org" target="_top">Eigen</a>
      and Boost.Ublas has a large volume of complex expression template code that
      cannot be reused elsewhere.
    </p>
<p>
      With the language facilities available in the C++14 and C++17 standards, an
      expression template library is now straightforward to write and use, and has
      very reasonable compile times.
    </p>
<p>
      As a quick example, let's say we are doing a bit of matrix math, and we write
      this statement:
    </p>
<pre class="programlisting"><span class="identifier">D</span> <span class="special">=</span> <span class="identifier">A</span> <span class="special">*</span> <span class="identifier">B</span> <span class="special">+</span> <span class="identifier">C</span><span class="special">;</span>
</pre>
<p>
      in which all the variables are matrices. It turns out that making a temporary
      for <code class="computeroutput"><span class="identifier">A</span> <span class="special">*</span>
      <span class="identifier">B</span></code> and then another temporary for
      the resulting product plus <code class="computeroutput"><span class="identifier">C</span></code>
      is very inefficient. Most matrix math libraries will have a single function
      that does it in one go:
    </p>
<pre class="programlisting"><span class="identifier">mul_add_assign</span><span class="special">(</span><span class="identifier">D</span><span class="special">,</span> <span class="identifier">A</span><span class="special">,</span> <span class="identifier">B</span><span class="special">,</span> <span class="identifier">C</span><span class="special">);</span>
</pre>
<p>
      If you use a matrix library that offers both kinds of syntax, you have to notice
      when some bit of operator-using code should be replaced with some more efficient
      function; this is tedious and error-prone. If the library does not provide
      the operator syntax at all, only providing the more-efficient function calls,
      code using the library is a lot less writable and readable.
    </p>
<p>
      Using Boost.YAP, you can write some library code that enables expressions like
      <code class="computeroutput"><span class="identifier">D</span> <span class="special">=</span>
      <span class="identifier">A</span> <span class="special">*</span> <span class="identifier">B</span> <span class="special">+</span> <span class="identifier">C</span></code>
      to be automatically transformed into expressions like <code class="computeroutput"><span class="identifier">mul_add_assign</span><span class="special">(</span><span class="identifier">D</span><span class="special">,</span>
      <span class="identifier">A</span><span class="special">,</span> <span class="identifier">B</span><span class="special">,</span> <span class="identifier">C</span><span class="special">)</span></code>.
    </p>
<p>
      Consider another example. Many of us have used Unix command line tools to remove
      duplicate lines in a file:
    </p>
<pre class="programlisting"><span class="identifier">sort</span> <span class="identifier">file_with_duplicates</span> <span class="special">|</span> <span class="identifier">uniq</span> <span class="special">&gt;</span> <span class="identifier">file_without_duplicates</span>
</pre>
<p>
      We can do something very similar with the standard algorithms, of course:
    </p>
<p>
</p>
<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special">&lt;</span><span class="keyword">int</span><span class="special">&gt;</span> <span class="identifier">v1</span> <span class="special">=</span> <span class="special">{</span><span class="number">0</span><span class="special">,</span> <span class="number">2</span><span class="special">,</span> <span class="number">2</span><span class="special">,</span> <span class="number">7</span><span class="special">,</span> <span class="number">1</span><span class="special">,</span> <span class="number">3</span><span class="special">,</span> <span class="number">8</span><span class="special">};</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">sort</span><span class="special">(</span><span class="identifier">v1</span><span class="special">.</span><span class="identifier">begin</span><span class="special">(),</span> <span class="identifier">v1</span><span class="special">.</span><span class="identifier">end</span><span class="special">());</span>
<span class="keyword">auto</span> <span class="identifier">it</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">unique</span><span class="special">(</span><span class="identifier">v1</span><span class="special">.</span><span class="identifier">begin</span><span class="special">(),</span> <span class="identifier">v1</span><span class="special">.</span><span class="identifier">end</span><span class="special">());</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special">&lt;</span><span class="keyword">int</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="identifier">v2</span><span class="special">(</span><span class="identifier">v1</span><span class="special">.</span><span class="identifier">begin</span><span class="special">(),</span> <span class="identifier">it</span><span class="special">);</span>
<span class="identifier">assert</span><span class="special">(</span><span class="identifier">v2</span> <span class="special">==</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special">&lt;</span><span class="keyword">int</span><span class="special">&gt;({</span><span class="number">0</span><span class="special">,</span> <span class="number">1</span><span class="special">,</span> <span class="number">2</span><span class="special">,</span> <span class="number">3</span><span class="special">,</span> <span class="number">7</span><span class="special">,</span> <span class="number">8</span><span class="special">}));</span>
</pre>
<p>
    </p>
<p>
      However, it would be much better if our code did exactly that, but with a more
      concise syntax:
    </p>
<p>
</p>
<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special">&lt;</span><span class="keyword">int</span><span class="special">&gt;</span> <span class="identifier">v1</span> <span class="special">=</span> <span class="special">{</span><span class="number">0</span><span class="special">,</span> <span class="number">2</span><span class="special">,</span> <span class="number">2</span><span class="special">,</span> <span class="number">7</span><span class="special">,</span> <span class="number">1</span><span class="special">,</span> <span class="number">3</span><span class="special">,</span> <span class="number">8</span><span class="special">};</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special">&lt;</span><span class="keyword">int</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="identifier">v2</span> <span class="special">=</span> <span class="identifier">sort</span><span class="special">(</span><span class="identifier">v1</span><span class="special">)</span> <span class="special">|</span> <span class="identifier">unique</span><span class="special">;</span>
<span class="identifier">assert</span><span class="special">(</span><span class="identifier">v2</span> <span class="special">==</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special">&lt;</span><span class="keyword">int</span><span class="special">&gt;({</span><span class="number">0</span><span class="special">,</span> <span class="number">1</span><span class="special">,</span> <span class="number">2</span><span class="special">,</span> <span class="number">3</span><span class="special">,</span> <span class="number">7</span><span class="special">,</span> <span class="number">8</span><span class="special">}));</span>
</pre>
<p>
    </p>
<p>
      This looks much more similar to the Unix command line above. (Let's pretend
      that <a href="https://github.com/ericniebler/range-v3" target="_top">Range-v3</a>
      doesn't already do almost exactly this.)
    </p>
<p>
      Boost.YAP can be used to do both of these things, in a pretty small amount
      of code. In fact, you can jump right into the <a class="link" href="boost_yap/manual.html#boost_yap.manual.examples.pipable_algorithms" title="Pipable Algorithms">Pipable
      Algorithms</a> example if you want to see how the second one can be implemented.
    </p>
<h4>
<a name="boost_yap.introduction.h1"></a>
      <span class="phrase"><a name="boost_yap.introduction.features"></a></span><a class="link" href="yap.html#boost_yap.introduction.features">Features</a>
    </h4>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          Simple <a class="link" href="boost_yap/concepts.html#boost_yap.concepts.expressiontemplate">ExpressionTemplate</a>
          and <a class="link" href="boost_yap/concepts.html#boost_yap.concepts.expression">Expression</a> concepts
          easily modeled by user code. Member and non-member functions on <a class="link" href="boost_yap/concepts.html#boost_yap.concepts.expressiontemplate">ExpressionTemplates</a>
          and <a class="link" href="boost_yap/concepts.html#boost_yap.concepts.expression">Expressions</a> can
          be added with compact macros, and a reference template that models <a class="link" href="boost_yap/concepts.html#boost_yap.concepts.expressiontemplate">ExpressionTemplate</a>
          exists for prototyping or experimentation.
        </li>
<li class="listitem">
          Evaluation of Boost.YAP expressions matches the semantics of builtin C++
          expressions as closely as possible. This leads to clearer understanding
          of the semantics of expression evaluation, because the definitions are
          local to the types involved.
        </li>
<li class="listitem">
          Expressions may be transformed explicitly in a user-defined way. This is
          accomplished with overloaded call operators in a transform class, which
          are matched against subexpressions in the overall expression. While these
          member functions may transform a subexpression into anything, a common
          pattern is to transform only some subexpressions into either new subexpressions
          or appropriate values and to leave other subexpressions unchanged. This
          <code class="computeroutput"><span class="identifier">evaluate</span><span class="special">(</span><span class="identifier">transform</span><span class="special">(</span><span class="identifier">expr</span><span class="special">))</span></code>
          idiom is expected to be one of the most common ways of using Yap to manipulate
          and evaluate expressions.
        </li>
<li class="listitem">
          Functions that operate on or create expressions. Functions are provided
          (and used within Boost.YAP) that manipulate expressions or their subexpressions.
          These simplify the process of writing user-defined transforms, for example.
        </li>
</ul></div>
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